A note on the dqds algorithm with Rutishauser's shift for singular values

DOI10.1007/s13160-011-0037-xzbMath1231.65067OpenAlexW2077978723MaRDI QIDQ645271

Kazuo Murota, Takayasu Matsuo, Kensuke Aishima

Publication date: 14 November 2011

Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13160-011-0037-x

zbMATH Keywords

iterative methodnumerical linear algebrasingular value

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15)

Related Items (2)

Discrete Lotka-Volterra with shift algorithm for computing matrix eigenvalues and singular values ⋮ A shift strategy for superquadratic convergence in the dqds algorithm for singular values

Uses Software

• LAPACK
• DLASQ

Cites Work

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• Rigorous proof of cubic convergence for the dqds algorithm for singular values
• Superquadratic convergence of DLASQ for computing matrix singular values
• Accurate singular values and differential qd algorithms
• Multiple representations to compute orthogonal eigenvectors of symmetric tridiagonal matrices
• An implementation of the dqds algorithm (positive case)
• A shift strategy for superquadratic convergence in the dqds algorithm for singular values
• On Convergence of the DQDS Algorithm for Singular Value Computation
• LAPACK Users' Guide
• Orthogonal Eigenvectors and Relative Gaps
• Über eine kubisch konvergente Variante der LR‐Transformation

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